A094566 Triangle of binary products of Fibonacci numbers.

1, 1, 2, 3, 4, 5, 8, 9, 10, 13, 21, 24, 25, 26, 34, 55, 63, 64, 65, 68, 89, 144, 165, 168, 169, 170, 178, 233, 377, 432, 440, 441, 442, 445, 466, 610, 987, 1131, 1152, 1155, 1156, 1157, 1165, 1220, 1597, 2584, 2961, 3016, 3024, 3025, 3026, 3029, 3050, 3194, 4181

Offset

1,3

Comments

For n>1, row n consists of n numbers, first F(2n-2) and last F(2n-1).

Central numbers: (1,4,9,25,64,...), essentially A081016.

Row sums: A027991. Alternating row sums: 1,1,4,4,30,30,203,203; the sequence b=(1,4,30,203,1394,...) is A094567.

In each row, the difference between neighboring terms is a Fibonacci number.

Links

Table of n, a(n) for n=1..55.

Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly 42:1 (2004), pp. 28-35.

Formula

Row 1 is the single number 1. For m>=1, Row 2m: F(2)F(4m-2), F(4)F(4m-4), ..., F(2m)F(2m), F(2m+1)F(2m-1), F(2m+3)F(2m-3), ..., F(4m-1)F(1) Row 2m+1: F(2)F(4m), F(4)F(4m-2), ..., F(2m+1)F(2m+1), F(2m+3)F(2m-1), F(2m+5)F(2m-3), ..., F(4m+1)F(1)

Example

Rows 1 to 4:
1
1 2
3 4 5
8 9 10 13

Prog

(PARI) pef(k, n) = fibonacci(2*k)*fibonacci(2*n-2*k);
pof(k, n) = fibonacci(2*n-2*k+1)*fibonacci(2*k-1);
tabl(nn) = {for (n=1, nn, if (n==1, print1(1, ", "), if (n % 2 == 0, for (k=1, n/2, print1(pef(k, n), ", "); ); forstep (k=n/2, 1, -1, print1(pof(k, n), ", "); ); , for (k=1, n\2, print1(pef(k, n), ", "); ); forstep (k=n\2+1, 1, -1, print1(pof(k, n), ", "); ); ); ); print(); ); } \\ Michel Marcus, May 04 2016

Crossrefs

Cf. A000045, A094565, A094567, A094568.

Sequence in context: A259185 A102471 A243490 * A190018 A217349 A329574

Adjacent sequences: A094563 A094564 A094565 * A094567 A094568 A094569

Keyword

nonn,tabl

Author

Clark Kimberling, May 12 2004

Status

approved